Continuous casting of strands using thermal stress reinforcement

ABSTRACT

Surfaces are reinforced against loads applied to one side by subjecting the opposite side to intense and continuous cooling to establish thermal stresses. This technique is applied in the continuous casting of slabs and billets by giving the slab and billet an initial concavity or at least restraining same from initial convexity and then subjecting its outer surface to the action of continuous and intense coolant sprays.

United States Patent 1 Rossi [451 Nov. 20, 1973 CONTINUOUS CASTING OF STRANDS USING THERMAL STRESS REINFORCEMENT Inventor:

Irving Rossi, Dunros Farm, James St., Morristown, NJ. 07960 Filed: Nov. 18, 1971 Appl. No.: 199,988

US. Cl. 164/89, 164/282 Int. Cl B22d 11/12 Field of Search 164/82, 89, 282, 164/283 References Cited UNITED STATES PATENTS 4/1963 Steigerwald 164/82 10/1967 Brondyke et al. 164/282 X 12/1968 Pearson 164/82 X 7/1970 Hess 164/283 zz zotd l 3,642,057 2/1972 Scheufele l64/283 FOREIGN PATENTS OR APPLICATIONS 1,508,802 l1/l969 Germany 164/273 729,490 5/1955 Great Britain... 164/273 783,365 9/1957 Great Britain 164/89 Primary ExaminerR. Spencer Annear Attorney-Nichol M. Sandoe et al.

[57] ABSTRACT Surfaces are reinforced against loads applied to one side by subjecting the opposite side to intense and continuous cooling to establish thermal stresses. This technique is applied in the continuous casting of slabs and billets by giving the slab and billet an initial concavity or at least restraining same from initial convexity and then subjecting its outer surface to the action of continuous and intense coolant sprays.

12 Claims, 14 Drawing Figures (KO 5) O O O O r 81%,, O O} F F; 2 25 O O O 0 atented Nov. 20, 1973 3 Sheets-Sheet 2 Q wmvm Patented Nov. 20, 1973 3,773,099

3 Sheets-Sheet 5 52 TIL E2. 11.

CONTINUOUS CASTING OF STRANDS USING THERMAL STRESS REINFORCEMENT This invention relates to the reinforcement of surfaces against forces acting transversely thereto, and more particularly it concerns novel application of thermal stresses to maintain desired surface configuration on structures subjected to internal pressures.

In its broadest aspects, the present invention is carried out by rapidly cooling the side of the structural surface which faces away from the transversely acting forces and maintaining this rapid cooling by an amount sufficient to set up thermal stresses which act in the plane of the surface to resist the transverse forces. As the thermal stresses begin to develop, any initial surface deflection is directed against the transversely acting forces so that any transverse components of the thermal stresses will be directed against the transverse forces.

The present invention is particularly advantageous in connection with the continuous casting of metal strands such as slabs (having an essentially rectangular cross-section) and billets or blooms (having a general square cross-section). In the continuous casting of these strands, molten metal is poured into the top of an open mold which is shaped to define the cross-section of the strand, i.e., the slab or billet, being cast. An outer shell forms inside the mold and this shell, which encloses a still molten core, is pulled continuously from the bottom of the mold.

Previously developed techniques of continuous casting are described in copending applications Ser. No. 111,488 filed Feb. 1, 1971, Ser. No. 114,592 filed Feb. 11,1971, Ser. No. 136,814 field Apr. 23. 1971 and Ser. No. 187,306 filed Oct. 7, 1971, of the present inventor. Those same applications described various novel techniques for reinforcing the wide sides of cast slabs against the bulging forces caused by the high ferrostatic pressure from the still molten core of the strand. In general, those reinforcing techniques make use of the compression strength of the outer shell of the slab being cast; and they involve shaping the wide sides of the slab to curve inwardly to form arches and, at the same time, squeezing the narrow sides in toward each other to maintain the arched configuration. The maintenance of an arch in this fashion enables the compressive strength of the outer shell to be utilized in resisting the outward bulging forces of the molten core.

The present invention provides a completely different type of surface reinforcement which does not depend upon the compressive strength of the arch of the outer shell of the strand being cast. According to the present invention, reinforcement is obtained by introducing thermal stresses in the outer shell of the strand and then directing the effects of these stresses so that they act in opposition to, rather than in conjunction with, the bulging forces of the pressurized molten core.

As illustratively embodied herein, the present invention may be carried out by rapidly cooling the outer surfaces of a strand as it exits from a mold; and at the same time restraining the surfaces against initial convexity which internal ferrostatic pressures tend to produce. This may be done by introducing at least a slight inward concavity to these outer surfaces to give direction to effects of the rapid cooling. In certain situations the sides may merely be held straight. The rapid cooling produces thermal stresses which shrink the outer surfaces of the shell of the strand being cast. These thermal stresses, which are extremely powerful, result in a bending of the shell walls. By introducing an initial concavity into the shell walls, the bending produced by the thermal stresses is directed to maintain this concavity. Furthermore, by properly controlling the cooling rate of the strand, the amount of thermal stress may be increased or decreased to increase or decrease the pitch of the arch. In continuous casting operations where strands such as slabs or billets are pulled downwardly from a mold, their molten cores experience a ferrostatic pressure which increases downwardly away from the mold. It is possible, with the present invention, to control the rate at which heat is withdrawn from the strand so that the thermal stresses will support the outer shell against the initially low ferrostatic pressure and thereafter to allow the increased ferrostatic pressure to force the slab sides outwardly to a flat condition suitable for rolling.

There has thus been outlined rather broadly the more important features of the invention in order that the detailed description thereof that follows may be better understood, and in order that the present contribution to the art may be better appreciated. There are, of course, additional features of the invention that will be described hereinafter and which will form the subject of the claims appended hereto. Those skilled in the art will appreciate that the conception upon which this disclosure is based may readily be utilized as a basis for the designing of other structures for carrying out the several purposes of the invention. It is important, therefore, that the claims be regarded as including such equivalent construction as do not depart from the spirit and scope of the invention.

Specific embodiments of the invention have been chosen for purposes of illustration and description, and are shown in the accompanying drawings, forming a part of the specification wherein:

FIG. 1 is a diagrammatic view illustrating the action of a uniformly distributed load on a structure supported according to the prior art;

FIG. 2 is a diagrammatic view illustrating a previously developed reinforcing technique for reinforcing structures against the action of a uniformly distributed load;

FIG. 3 is a diagrammatic view illustrating the technique of the present invention for reinforcing a structure against the action of a uniformly distributed load;

FIG. 4 is a side elevational view of a continuous casting system, in operation, in which the present invention is embodied;

FIG. 5 is a side elevational view of the continuous casting apparatus of H6. 4;

FIGS. 6, 7, 8 and 9 are section views taken respectively, along lines 6-6, 7l-7, 8-8 and 9-9 of HG.

FIGS. 10 and 11 are cross section views similar to FIG. 7 but showing alternate initial shaping roll configurations;

FIG. 12 is a perspective view illustrating how roll arrangements of the prior art may be utilized with the present invention;

FIG. 13 is a cross sectional view of a billet forming mold in which a billet is continuously casting according to the present invention; and

FIG. 14 is a cross sectional view showing a billet support and cooling arrangement in accordance with the present invention.

In the diagram of FIG. I, a shell section 10, which may be, for example, a section of solidified metal which defines the outer surface of a casting during cooling thereof, is shown as supported on one side at two end points 12 and 14 by upwardly directed support force vectors Fs. A uniformly distributed load, represented by a plurality of small downwardly extending load force vectors Pi is applied to the other side of the section 10. This uniformly distributed load may be developed, for example by the ferrostatic pressure of the still molten core portion of a metal casting as it pushes outwardly against the outer solidified shell.

Now, where the section is either too thin or is too soft to resist the effects of the uniformly distributed force vectors Fi, it will, when supported only at its two end points 12 and 14, begin to sag or bulge as indicated in dashed outline in FIG, 1.

FIG. 2 illustrates a previous approach to prevent the above-described sagging or bulging action. As can be seen in FIG. 2, the shell section 10 is given an initial arch-like configuration in the direction of the uniformly distributed load. This arch-like configuration is maintained by orientating the support force vectors F s so that they angle in toward each other. With this arrangement, the arch-like shape of the shell section serves to divert the uniformly distributed load force vectors Fi along the plane of the shell section where they are resisted by the inwardly angled support force vectors Fs.

While the arched configuration in FIG. 2 serves to increase the resistance of the shell section 10 to the bulging effects of the load force vectors Fi, this arrangement is subject to two conditions, namely the compressive or column strength of the shell section itself, and the availability of some external means for maintaining the externally supplied angled support force vectors Fs.

FIG. 3 illustrates the manner in which the present invention serves to overcome the above two limiting conditions. As can be seen in FIG. 3, there are provided a plurality of coolant spray nozzles 16 which direct intense sprays of collant against the shell section 10 on the side opposite to that wehre the load force vectors Fi are applied. The sudden cooling of the lower shell section surface produces thermal stresses within the material of the shell section, as illustrated by the tangentially oriented thermal stress vectors Ft. These thermal stress vectors cause the shell section to shrink especially at its outer surface. The inner surface of the shell section, where the load force vectors F1 are applied, is not subjected to the intense cooling action of the sprays from the nozzles 16. Accordingly, a temperature differential is set up across the thickness of the shell section which causes it to bend and automatically assume an arch-like configuration, as shown in FIG. 3.

It will be seen in FIG. 3 that the thermal stresses set up in the shell section 10 by the intense cooling action of the nozzle sprays tend to shrink the shell section. Thus, the arrangement of FIG. 3 is not subject to and, therefore, is not limited by, the compressive or column strength of the shell section itself as is the case with the arrangement of FIG. 2. In addition, since the stresses which maintain the arch-like configurations are generated within the material of the shell section itself, they render the arch-like configuration self-sustaining so that no special external support is required other than that needed to guide or support the overall casting.

FIGS. 49 illustrate the application of the abovedescribed thermal stress reinforcing principles to the continuous casting of a rectangularly cross-sectional slab of steel. Continuous casting of steel slabs is described in detail in the previously identified copending U. S. Pat. applications Ser. No. l 1 1,488, Ser. No. l 14,592 and Ser. No. 187,306. In this application, the process and apparatus will be described only with such detail as is required to illustrate the applications of the present invention to the process.

As can be seen in FIGS. 4 and 5, molten steel 20 is poured continuously into the top of a hollow mold 22 and a slab 24 of steel is pulled continuously downward from the bottom of the mold and is guided by various sets of rolls 26, along a path which extends first downwardly and then curves to the horizontal. A plurality of water spray nozzles 32 are provided to subject substantially the entire surface of the slab 24 to intense and continuous cooling.

The slab 24, upon exiting from the mold 22, is made up of an outer shell 34 which surrounds a central still molten core 36. As the slab proceeds downwardly from the mold and is cooled by water sprays from the nozzles 32, its outer shell 23 stiffens and thickens while the central core 36 correspondingly diminishes. In the past, it was found that the thickening and stiffening of the outer sheel 34 was insufficient to strenghten the slab against the increasing ferrostatic pressure which built up in the central core as the slab proceeded downwardly from the mold. As a result, the slab began to bulge along its wider faces. In order to prevent this, the prior art resorted to heavy rolls which, in effect, hot rolled the slab back to rectangular configuration. These rolls had to be quite large; and because they interfered with coolant application, and because they worked the outer surface of the slab, the slab did not cool in a continuous or uniform manner; and in fact the slab would undergo numerous temperature reversals as a result of passing through several sets of rolls. This tended to produce deleterious effects on the structural characteristics of the slab.

The present invention makes use of thermal stresses, introduced by suddenly applied and continuously maintained cooling of the surface of the slab to bring the slab itself to a self supporting condition.

It will be seen in FIGS. 4 and 5 that the coolant spray nozzles 32 are distributed so as to maintain a continuous spray of coolant liquid over substantially the entire outer surfaces of the slab 24. Whereas in prior continuous casting systems the size of the support rolls had to be so large and their spacing so close that the slab was to a great degree masked from the coolant, it will be noted in FIG. 5 that no such masking or interference occurs in the case of the present invention; and cooling is carried out in a continuous manner. As can be seen in FIG. 5 the rolls 26 contact only the outer edges of the slab 24, so that substantially the entire slab is exposed to coolant spray. Corresponding rolls 26 on opposite edges of the slab 24 are interconnected by an axle 38 which serves to synchronize their rotation and to maintain them in axial alignment. The axles 38, it will be noted, are quite small in diameter and they do not touch the slab 24. Accordingly no interference with the continuous spray cooling is produced by the axles 38.

FIG. 6 illustrates the initiation of slab formation and cooling inside the mold 22. As can be seen the mold is essentially a hollow jacket through which a coolant liquid is circulated. The coolant enters through an inlet 40 and leaves via an outlet 42. A central copper liner 44 forms the inner surfaces of the coolant jacket and defines the cross sectional shape to be formed by the mold, in this case rectangular.

The molten material which is poured into the mold is chilled by contact with the copper liner 44 and it begins to solidify in this region to form the outer shell 34 surrounding the still molten core 36.

The cooling and solidification of the shell 34 is accompanied by a shrinkage thereof and this shrinkage is greatest in the comer regions of the mold. This is because in the corner regions the material being cast experiences the highest ratio of mold cooling surface area to molten material volume. This accentuated corner shrinkage plus the outward push exerted by the molten core 36 against the very thin and as yet quite soft shell 34 in the central regions of the wide faces of the slab being formed causes the slab to tend toward an initial oval cross sectional shape with bulged wide sides 46 as shown in FIG. 6.

As the newly formed slab exits from the mold 22 it immediately encounters intense cooling sprays from the uppermost of the nozzles 32, as shown in FIGS. 5 and 6. The slab then passes between a set of bellied initial shaping rolls 48 which serve as shown in FIG. 7 to reverse the direction of bulging of the wide sides 46 of the slab. Since the ferrostatic head in the region of the initial shaping rolls 48 is relatively small and since the outer shell 34 is still rather thin and soft, these rolls do not encounter substantial resistance and accordingly they may be of small diameter. The initial concavity may, if desired, be provided by so shaping the wide sides of the mold itself; and in such case the rolls 48 are not necessary. Also, under certain conditions the initial concavity may be eliminated altogether so long as the wide sides of the slab are restrained against initial convexity or bulging caused by internal ferrostatic pressure.

As the slab 24 proceeds downwardly from the initial shaping rolls 48 it immediately encounters the full effects of the coolant sprays from the nozzles 32. This rapid cooling establishes high thermal stresses in the outer shell 34 which cause it to pull inwardly from end to end. Because however, the wide sides 46 have been directed inwardly toward each other in the form of arches, the thermal stresses act to sustain this arched configuration. Depending upon the intensity of cooling the rate of shell thickening may be controlled. This is especially advantageous since as the slab 24 progresses downwardly from the mold 22 the ferrostatic pressure within the molten core 36 builds up very rapidly and the tendency toward bulging along the wide sides 46 of the slab increases correspondingly. This increased bulging tendency may be compensated for by the controlled thickening of the outer shell 34. Because the shell itself is under thermal stress the overall restraining action of the shell is controlled by control of its thickness, which in turn is controlled by the intensity of cooling.

Conversely, the restraining action of the shell may be relieved by reducing the cooling action and thermal stresses produced by the nozzle sprays. This will decrease the resistance to bulging; and by proper control of the nozzle sprays the thermal stresses may be relieved sufficiently in the final cooling stage so that the ferrostatic pressures will bring the slab to a final desired configuration upon completion of solidification.

The final desired configuration of the slab will depend upon the subsequent processing to which it is subjected. In most cases the slab is rolled; and for this purpose a generally rectangular cross section is usually preferred. Other cross sections may be provided however by control of the intensity of cooling. In some cases it may be necessary only to maintain a slight concavity in the slab under thermal stress; and where that concavity is quite small, it may not be necessary to change the cooling to allow the ferrostatic pressure to bulge the sides out to a fully flattened condition. On the other hand, as indicated previously, the thermal stresses may be able to maintain the sides of the slab in flattened condition without any concavity being introduced or maintained.

As shown in FIG. 9 the slab 24 is guided in its movement donwwardly from the mold 22 and around to a horizontal direction by passing between the sets of rolls 26. These rolls, it will be noted, merely guide the slab and exert no reinforcing or shaping forces on its cross sectional configuration. They do however allow the outer surface of the slab to remain exposed to the direct action of the nozzle sprays.

FIGS. 10 and 11 illustrate alternate configurations of initial shaping rolls which can be used in place of the bellied rolls 48 shown in FIGS. 5 and 7. In FIG. 10 a set of double arched rolls 50 serve to produce a figure eight type cross sectional configuration to the slab. In FIG. 11, a set of double conical rolls 52 serve to produce an inward V-shape to the wide sides of the slab. These various configurations, including the inward arch produced by the belied initial shaping rolls 48, merely serve to give initial direction to the effects of the thermal stresses produced by the sudden cooling of the nozzle sprays. Thus the contours produced by these rolls may be very shallow, and need not be as accentuated as shown in these drawings.

FIG. 2 illustrates how the present invention may be practiced using a continuous casting system in which conventional uniform diameter rolls extending across the full width of the slab are employed. In such arrangements there is provided, of course, an initial shock cooling by the action of intense coolant sprays upon the slab 24 as it exits from the mold. This is carried out as described above. Also as previously described the initial shock cooling is coordinated with an initial shape guiding action which may, as described above, be provided with initial shaping rolls or it may be provided by shaping the mold itself with inwardly arched wide sides. In any event, the combination of the initial shaping and the sudden shock cooling sets up in the outer shell of the slab 24, high thermal stresses which serve to maintain inward concavities 60 along the wide sides of the slab. As the slab 24 passes downwardly between a pair of conventional straight sided rolls 62 there remains a space 64 between the roll surfaces and the concavities 60 of the slab. This space allows continuous flow of coolant liquid from the nozzles 32 so that it flows down along the slab between the slab and the rolls 62. Because of the open space between the rolls 62 and the slab surfaces it is possible to maintain the continuous cooling action over the entire slab surface which is required to maintain the thermal stresses which provide self support for the slab according to the present invention.

Turning now to FIGS. 13 and 14 there is seen an adaptation of the present invention to the formation of strands of metal known as billets. These billets are of generally square cross section. In the past difficulties have arisen as the billet tended to bulge along all four sides due to the effects of ferrostatic pressure acting through the molten core. in some cases that is the billet would shift to an out of square condition and diagonal shear stresses and faults would be developed.

With the present invention the difficulties described above are avoided. As can be seen in FIG. 13 there is provided, as shown in cross section, a billet forming mold 70 of essentially square cross section. The four sides of the mold 70 are arched inwardly as at 72 to provide an initial shaping. As described above in connection with the preceeding embodiment the sides of the mold 70 may be straight and initial shaping rolls may be provided to give direction to the deformations which will be produced by thermal stresses. In the mold 70, there is shown a billet 74 having an outer shell 76 and a central molten core 77. The molding action and the formation of the shell 76 are as described previously.

As the billet exits from the mold '70 it passes downwardly between corner support rolls 78, which, as shown in FIG. 14, engage only the corners of the billet and leave its four inwardly arched sides exposed to the action of a continuous and intense cooling action produced by sprays from nozzles 80. These sprays act, as described above to induce thermal stresses in the shell 76 so that the arched configurations become self supporting. No forces other than those needed for guidence are imposed on the corner support rolls 78.

It will be appreciated from the foregoing that the present invention provides a basically different means of reinforcing surfaces during a molding operation in that it makes use of the very high thermal stresses which occur during solidification of the material being cast. It will further be appreciated that the present invention takes advantage of phenomena not heretofore recognized as being useful, namely the extremely high thermal stresses which can be developed; and it directs these stresses in a novel manner so that they act to produce a self supporting effect which permits a reduction in the size and strength of the supporting apparatus. The thermal stresses may also be controlled anywhere along the cooling path simply by adjusting the temperature or the intensity of coolant spray at the selected locations.

In connection with each of the embodiments described above, the control of cooling obtained with the nozzle sprays also serves, in addition to the control of thermal stresses, to control the shell thickness. Thus, as greater cooling is maintained, the shell thickness will build up faster, and conversely, as cooling intensity is reduced, shell thickness buildup is also slowed down. in fact, the thickness of the shell may actually be decreased by reduction of cooling. This is because the molten core serves as a heat source at that high temperature. By reducing the cooling action of the coolant sprays the rate of heat transfer through the shell, from the molten core to the outer surface of the cast element is reduced. Consequently the temperature along the inner regions of the shell begins to rise and the material in this region reverts to a plastic or semi-liquid state. The thermal stresses in this region are lost and the shell wall thickness is thus effectively reduced. This thickness can, of course, be rebuilt by increasing the cooling intensity of the sprays.

As indicated previously the thermal stress reinforcing, which can be closely controlled by control of the intensity and temperature of the coolant action with the ferrostatic pressure effects of the molten central core to control the final shape of the completely solidified casting. Thus by reducing the intensity and/or temperature of the coolant sprays toward the lowermost regions of the casting path, the increased ferrostatic pressure of the molten core in these regions will act to bulge outwardly the inwardly arched sides of the outer shell. By proper coordination of the cooling intensity and the ferrostatic pressure a very substantial degree of contour control is obtained without any need for external rolling or forming operations.

It will thus be appreciated from the foregoing that the thermal stress reinforcing concept of the present invention is not limited to slabs and billets, but in fact, it may be applied to various other structural shapes, for example rounded outer configurations. Also, depending upon the amount of reinforcing needed, and the degree of thermal stress produced it may be possible, under certain conditions, to maintain an outer shell surface in a flat configuration during the solidification of the inner core, with the thermal stresses developed by the coolant sprays serving alone, without any compressive arch action, to resist the bulging effects of the molten core.

Having thus described the invention with particular references to the preferred forms thereof, it will be obvious to those skilled in the art to which the invention pertains, after understanding the invention, that various changes and modifications may be made therein without departing from the spirit and scope of the invention as defined by the claims appended thereto.

What is claimed is:

E. In a method of continuously casting a metal strand by pouring molten metal into the upper end of a tubular mold and continuously withdrawing from beneath said mold an elongated metal strand having a solid outer shell with sides surrounding an inner molten core, the steps of forming concavities in the sides of said outer shell, subjecting said sides to shock cooling by spraying onto said sides a coolant fluid at a sufficiently high intensity and at a sufficiently low temperature to establish, in said sides, thermal stresses which maintain said concavities in opposition to ferrostatic pressures exerted outwardly from the said core without mechanical bracing of said sides, said sprays being directed over a region of said sides where they are otherwise incapable of withstanding the bulging effects caused by pressure within said molten core, and maintaining said cooling continuously until said sides become sufficiently thick as to be self supporting.

2. A method according to claim 1 wherein said method of casting includes the continuous casting of a metal slab of essentially rectangular cross section.

3. A method according to claim 2 wherein said concavities are formed in the wider sides of said shell.

8. A method according to claim 1 wherein said method of casting includes the continuous casting of a metal billet of essentially square cross section.

5. A method according to claim 2 wherein the cooling is reduced in order to permit the heat remaining in the center of the slab to relieve a portion of the thermal stresses and allow ferrostatjc pressure to force the slab sides outwardly.

6. A method according to claim 3 wherein the span of each concavity is a single arch which spans the entire width of each wider side of said slab.

7. A method according to claim 3 wherein the span of each concavity is a single arch which spans less than the width of the wider sides of the slab.

8. A method according to claim 7 in which the wider sides of the slab are formed into several adjacent concavities.

9. A method according to claim 1 in which concavities are formed on more than one side of the strand.

10. A method according to claim 1 wherein the cooling is maintained in an amount to achieve a predetermined rate of solidification of the inner molten core.

11. A method according to claim 1 wherein the coolin is reduced prior to complete solidification of the core to permit the shell faces to be straightened by the ferrostatic pressure of the molten core.

12. A method according to claim 1 wherein the thermal stresses are intensified to increase the pitch of said concavities. 

1. In a method of continuously casting a metal strand by pouring molten metal into the upper end of a tubular mold and continuously withdrawing from beneath said mold an elongated metal strand having a solid outer shell with sides surrounding an inner molten core, the steps of forming concavities in the sides of said outer shell, subjectinG said sides to shock cooling by spraying onto said sides a coolant fluid at a sufficiently high intensity and at a sufficiently low temperature to establish, in said sides, thermal stresses which maintain said concavities in opposition to ferrostatic pressures exerted outwardly from the said core without mechanical bracing of said sides, said sprays being directed over a region of said sides where they are otherwise incapable of withstanding the bulging effects caused by pressure within said molten core, and maintaining said cooling continuously until said sides become sufficiently thick as to be self supporting.
 2. A method according to claim 1 wherein said method of casting includes the continuous casting of a metal slab of essentially rectangular cross section.
 3. A method according to claim 2 wherein said concavities are formed in the wider sides of said shell.
 4. A method according to claim 1 wherein said method of casting includes the continuous casting of a metal billet of essentially square cross section.
 5. A method according to claim 2 wherein the cooling is reduced in order to permit the heat remaining in the center of the slab to relieve a portion of the thermal stresses and allow ferrostatic pressure to force the slab sides outwardly.
 6. A method according to claim 3 wherein the span of each concavity is a single arch which spans the entire width of each wider side of said slab.
 7. A method according to claim 3 wherein the span of each concavity is a single arch which spans less than the width of the wider sides of the slab.
 8. A method according to claim 7 in which the wider sides of the slab are formed into several adjacent concavities.
 9. A method according to claim 1 in which concavities are formed on more than one side of the strand.
 10. A method according to claim 1 wherein the cooling is maintained in an amount to achieve a predetermined rate of solidification of the inner molten core.
 11. A method according to claim 1 wherein the coolin is reduced prior to complete solidification of the core to permit the shell faces to be straightened by the ferrostatic pressure of the molten core.
 12. A method according to claim 1 wherein the thermal stresses are intensified to increase the pitch of said concavities. 